How has Solve changed in 3.0.1?
- To: mathgroup at smc.vnet.net
- Subject: [mg8922] How has Solve changed in 3.0.1?
- From: "John E. Derwent" <John.E.Derwent.1 at nd.edu>
- Date: Sat, 4 Oct 1997 22:08:02 -0400
- Sender: owner-wri-mathgroup at wolfram.com
It seems that in 2.2 Solve knew that exponentials are never 0, but it doesn't in 3.0.1. Consider the problem of finding maxima and minima for the function f[x,y]=(x^2+3y^2)e^(-x^2-y^2). The critical points are given by Solve[Grad[f[x,y]]==0], i.e., Solve[-2x(-1+x^2+3y^2) e^(-x^2-y^2)==0, -2y(-3+x^2+3y^2) e^(-x^2-y^2)==0]. In 2.2 the output was the five solutions (0,0), (1,0), (-1,0), (0,1) and (0,-1), after a message about using inverse functions. In 3.0.1 the message about using inverse functions is there, there are also some messages about not being able to verify some solutions, and that limits may be necessary, and 16 more solutions are given. They are (-Infinity, -I Infinity), (-Infinity, I Infinity), (Infinity, -I Infinity), (Infinity,I Infinity), (0, -Infinity), (I Infinity, -Infinity) twice, (0, Infinity), (-I Infinity, Infinity) twice, (-I Infinity, Infinity) twice, (I Infinity, Infinity) twice, (x, -SqrtSqrt[1-y^2]), (x, SqrtSqrt[1-y^2]). The last two are not solutions unless y=1 or -1 and x=0, and it is a strain to consider the others as the solutions "in the limit". For example, why not include (Infinity, Infinity)? Does anyone know what has changed in Solve? I can find no explanation in the book or in the Help. Everything there seems to suggest only finite solutions. Of course the exponential term could be factored out before solving, but why should that be necessary now when it wasn't before?